The article doesn't describe the way to avoid the difference in rectangle size in a cubesphere, so let me.
The bad way: - Generate a cube - Subdivide each face using linear interpolation (lerp) - Normalize each vector to put it on a unit sphere
The good way: - Generate a cube - Subdivide using spherical linear interpolation (slerp) - done!
The cubesphere has lots of interesting geometric properties, particularly in texture mapping.